International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN 2249-6890 Vol. 2 Issue 4 Dec - 2012 1-10 © TJPRC Pvt. Ltd.,
THERMODYNAMICS MODELING OF AUTOMOBILE EVAPORATIVE AIR CONDITIONING (EVAPORATIVE TEST RIG) WITH RESULT AND DISCUSSION, WHEN AUTOMOBILE VELOCITY IS 60KM/HR 1 1
R.RAJVAIDYA & 2S.P.S. RAJPUT
Department of Mechanical, BUIT, BU, Bhopal, M.P, India 2
Department of Mechan Mechanical, MANIT, Bhopal, M.P, India
ABSTRACT This paper presents the thermodynamics modeling of automobile evaporative air conditioning (evaporative test rig)with result and discussion, when automobile velocity is 60K.m/hr. Modeling of the thermodynamics process involves in evaporative test rig, as and when it is attach on automobile roof. Condition to be followed, is that velocity of automobil automobile is 60K.m/hr. Formula base calculation of thermodynamics thermodynamics properties with respect to the velocity of automobile, result of output condition are display by table.
KEYWORDS: Automobile Evaporative Air Conditioning (Evaporative Test Rig), Physical Properties, Psychrometric Formulae, Thermodynamics Modeling, Thermodynamics Properties Like Dry Bulb Temperatu Temperature, Enthalpy, Relative Humidity
INTRODUCTION Thermodynamics modeling of a real evaporative test rig (E.T.R) attached on the roof of automobile which actuate a set of thermodynamics (psychrometric) formulas. Success in process modeling [1] is critically dependent upon accurate descriptions of the thermodynamic properties and phase behavior of the concerned designed systems. A perspective is offered here on applied thermodynamics from a research viewpoint. Modeling Modeling is a key enabling technology for process development and design, equipment sizing and rating, and processed bottlenecking and optimization. Thermodynamics modeling is a technological tool of creating a virtual environment of evaporative test rig to sstudy its performance. Formulae base procedure to calculate psychrometric terms (dry bulb temperature, relative humidity, and specific humidity), flow of energy (heat), and mass (air and water), etc. Modeling foundation is laid by arranging the fundamental thermodynamics formulae with respect to E.T.R “ Figure1” fabricated geometrical design condition; then the approach is in successfully execute the psychrometric relation and process. All the result and discussion are developed under a given condition that vehicle speed is 60Km/hr.
Figure 1: Drawing Picture off Automobile (Wagon-R) (Wagon Loaded with Evaporative Test Rig with ith Ambient Air Flowing Inside Show Indiviual Formulation Process 1 to Process 18.
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R.Rajvaidya & S.P.S. Rajput
METHODS Formulae [2] (Ideal) Theoretical calculations. Ideal working of Evaporative Test Rig (E.T.R [3]) when, V1= Velocity of automobile: Km/hr; tdb1=Ambient Air dry bulb temperature: 0C; φ1=Ambient Air Relative humidity: %; A1 =Area of the face Duct of E.T.R. [3] through which ambient air is entering as M1: =Total height ×Total width of the Duct face − Border height × Border width Present on Duct face Total height = 31 cm. = 0.31 m. Total width = 80 cm. = 0.80 m. Border thickness along width's = 1.5 cm. + 1.5cm. Or 2× (1.5cm.) = 3 cm. = 0.003 m. Border thickness along the heights =9 cm + 9 cm. = 18 cm. = 0·18 m. (1). So (A1) Area of the faces Duct of E.T.R [3]. = 0·31 x 0·80 − 0·03 x 0·18 = 0·2426 m2
------- (i)
V1 = Velocity (through or by) which automobile is moving or velocity by which atmospheric (or) ambient air is bleed inside the area of Duct face of E.T.R.. (2).
V1 = 20 km/hr to 60 km/hr. OR 20 x 16·6 m/min to 60 x 16·6m/min. (3).
3
ρ1= Density (Kg/m ): = 1/vg =
------ (ii) ------ (iii)
Specific volume of the moist air [4] is given by (3a). Vg=287·2×tdb1 / [(Pa−Pv) ×105]
------ (iii.a)
Where vg is m3/kg of dry air; and tdb1 in Kelvin (4). tdb=Dry bulb temperature; tdb1=273+℃ (5). Dalton law of partial pressure P=Pa+Pv ; Where P=atmosphere pressure (1bar); Pa=partial pressure of air; Pv=partial pressure of water vapour; Pa, Pv; pressure in bar and P=1bar, therefore Pa is
-------- (a1)
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Thermodynamics Modeling of Automobile Evaporative air Conditioning (Evaporative Test Rig) with Result and Discussion, When Automobile Velocity is 60km/Hr
-------- (b1)
(5a). Pa=P−Pv Substituting the value of Pa from equation (b1) in (iii.a), therefore: Vg=287·2×tdb1 / [{P−Pv −Pv} ×105] Vg=287·2×tdb1 / [{P− (2×Pv)} ×105]
(Or) Specific volume can be located in psychometric chart [5] when point conditioning are defined i.e. tdb1 dry bulb temperature; φ1 Relative humidity. Now, (6).M1 = Mass of the ambient air or atmospheric air entering the front face of evaporative cooler unit (E.C.U) or E.T.R. M1 = Density x Area of the E.T.R. × Velocity of automobile
------- (iv)
M1 = ρ1 × A1 × V1 (7).
First of all, we have we will take data of dry bulb temperature (tdb1) & relative humidity (ϕ1) from climate, weather report[6] and the measuring instrument (Hygrometer [7]).
(8).
Then we use formula
------- (v)
ϕ1 = =
ϕ1= Pv1/Ps1 Here Ps1 is taken from Steam Tabl Table [8] at dry bulb temperature (DBT) tdb1and relative humidity ϕ1 data is taken from climate weather report substituting the value in equation (v). It will give Pv1: bar (9)
Now, we calculate W1 by using the formula: W1=0.622×Pv1/Pb-Pv1 W 1= 0.622
------ (vi)
Where W1 is specific humidity of ambient air or atmospheric air at the inlet of face duct; (kg/kg. of dry air). Here putting the values of Pv1 in bar and Pb = 1bar in equation (vi) gives us W 1=can be calculated (10)
Now, we will calculate W2 from the formula which is obtained from psychrometric process of Cooling and
humidification by water injection (evaporative cooling) [9].
Figure 2: Cooling and Humidification by Water Injection
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R.Rajvaidya & S.P.S. Rajput
The formula (mass balance),
W2 =
W1 +
mw ma
W 2 = W 1 + mW ma
---- (vii)
------ (vii)
Where: mw = Mass of the water supplied or circulated[10] by submersible pump in E.T.R.; kg/min. ma = Mass of dry air, kg/kg of dry air W1 = Specific humidity of entering air, already calculated W2 = Specific humidity of leaving air or specific humidity at point 2 inside the automobile console or cabin, (11)
Since
W 1 = mv ma
Here
mv = mass of the water vapour.
Since W 1 (kg/kg of dry air) = is calculated from the equation (vi). Therefore
mv = ma×W1
------- (viii)
As we know, Total mass flow rate = Mass of the dry air + Mass of the water vapour M1 = ma + mv
-------
(ix)
-----
(x)
--------
(xi)
Here M1 = total man flow rate of Most air; kg/min. already calculated from the equation (iv). Substituting the value of equation (viii) in equation (ix) M1 = ma + ma W 1 M1 = ma (1 + W 1) ma = M1/ ( 1+ W 1) ma = can be obtained from equation (x). Hence W 2 can be determine by Substituting the value of W1, ma and mw=6·5kg/60min. in equation (vii). (12) Now we will calculate Pv2 by Substituting the value of W 2 in the psychrometric formula:W 2 = 0.622 Pv2/Pb-Pv2 As Pb = 1 bar for equation (xi). (13) Now t2 can be calculate from the carrier equation [4] formula Pv2= Pw2
- (Pb-Pw2) (t2 - tw2) 1544 - 1.44 tw2
t2 =tdb2= dry bulb temperature at point 2 inside the car console. Pb = 1 bar;
-------- (xii)
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Thermodynamics Modeling of Automobile Evaporative air Conditioning (Evaporative Test Rig) with Result and Discussion, When Automobile Velocity is 60km/Hr
Pv2= is obtained from equation (xi) Here Pw2 can be obtained from the stem table at tw2. Since we follow constant enthalpy line in psychometric chart because the psychometric process is cooling and humidification [11] by water injection (evaporative cooling) so wet bulb temperatures remain constant. So
tw1 = tw2.
------ (xiii)
(14) tw1 can be obtained from psychometric chart (or) can be formulated , From psychrometry corresponding to point 1, when we have tdb1= dry bulb temperature and φ1 = relative humidity are known. Here is the formula to calculate tw1. (15)
First h = specific enthalpy is to be calculated by the below formula h= specific enthalpy [4], [12] of ambient air
Formula: - h=ha+ϕ (hs−ha) Given
-------- (xiv)
ϕ1=relative humidity of ambient air; %
ha= specific enthalpy of dry air ;kJ/kg ha=cpa × tdb1 Given
---------- (xv)
cpa= Specific heat of dry air 1.005kJ/kgk
Given
tdb1 = dry bulb temperature; ℃
hs=specific enthalpy of 100% saturated mixture(dry air+water vapour). hs = specific enthalpy of 100% saturated mixture[13] corresponding to dry bulb temperature.tdb1 from ;Table.1 Substituting the value of Cpa, tdb1 in equation (xv) to calculate ha. Now substituting the valve of ha, ϕ1, hs in equation (xiv), on solving, specific enthalpy of ambient air (h) kJ/kg is calculated. Wet bulb temperature (tw1) corresponding to h (specific enthalpy of ambient air) [13] can be obtain from Table.1 (16) Now, t2 (dry bulb temperature) is to be calculate by substituting the valve of tw1=tw2, Pw2, Pb, in the equation (xii)
Pv2= Pw2
- (Pb-Pw2) (t2 - tw2)
-------- (xii)
1544 - 1.44 tw2 Now, from the relative humidity formula ---------- (xvi) Now, Ps2 can be obtained from steam table at t2, substituting the valve of Ps2 and Pv2 in equation (xvi)
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R.Rajvaidya & S.P.S. Rajput
We will calculate ϕ2; relative humidity of leaving air or specific humidity at point 2 inside the automobile console or
cabin, inside the Car console
To determine φ2 & t2 by proceeding through psychrometric chart: (17) Now, by taking W1as a point of reference, going along constant enthalpy line in psychometric chart and locate the point corresponding to W 2. Now, from the psychrometric chart, t2 & φ2 can be easily determined.
Figure 3: Psychrometric Chart Table 1: Saturated Properties of Moist Air Having Vapour Pressure in Various Units [13]. T
T
WS
hS
vS
p
p
p psia
p mm of Hg
p inch of Hg
o
C
K
kJ/kg
m3/kg
bar
ata
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5
274 275 275 276 276 277 277 278 278 279 279 280 280 281 281 282 282 283 283 284 284 285 285 286 286 287
kg/kg of dry air 0.0041 0.0042 0.0044 0.0045 0.0047 0.0049 0.005 0.0052 0.0051 0.0056 0.0058 0.006 0.0062 0.0064 0.0067 0.0069 0.0071 0.0074 0.0076 0.0079 0.0082 0.0085 0.0087 0.009 0.0093 0.0097
11.19 12.07 12.96 13.87 14.79 15.72 16.67 17.63 18.61 19.6 20.61 21.64 22.68 23.74 24.81 25.91 27.02 28.15 29.31 30.48 31.67 32.89 34.12 35.38 36.67 37.97
0.782 0.784 0.785 0.787 0.789 0.79 0.792 0.794 0.795 0.797 0.799 0.8 0.802 0.804 0.805 0.807 0.809 0.811 0.812 0.814 0.816 0.818 0.82 0.821 0.823 0.825
0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.009 0.009 0.009 0.01 0.01 0.01 0.011 0.011 0.011 0.012 0.012 0.013 0.013 0.014 0.014 0.014 0.015 0.015
0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.009 0.009 0.009 0.01 0.01 0.01 0.011 0.011 0.011 0.012 0.012 0.013 0.013 0.013 0.014 0.014 0.015 0.015 0.016
0.1 0.1 0.1 0.11 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.19 0.2 0.2 0.21 0.22 0.22
4.92 5.1 5.29 5.48 5.68 5.88 6.09 6.51 6.53 6.77 7 7.25 7.5 7.77 8.03 8.31 8.6 8.9 9.2 9.51 9.83 10.2 10.5 10.9 11.2 11.6
0.19 0.2 0.21 0.22 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.39 0.4 0.41 0.43 0.44 0.46
p ft of water 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5
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Thermodynamics Modeling of Automobile Evaporative air Conditioning (Evaporative Test Rig) with Result and Discussion, When Automobile Velocity is 60km/Hr
T
T
WS
hS
vS
p
p
p psia
p mm of Hg
p inch of Hg
o
C
K
kJ/kg
m3/kg
bar
ata
14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0
287 288 288 289 289 290 290 291 291 292 292 293 293 294 294 295 295 296 296 297 297 298 298 299 299 300 300 301 301 302 302 303 303 304 304 305 305 306 306 307 307 308 308 309 309 310 310 311 311 312 312 313 313 314 314
kg/kg of dry air 0.01 0.0103 0.0107 0.011 0.0114 0.0118 0.0122 0.0125 0.013 0.0134 0.0138 0.0143 0.0147 0.0152 0.0157 0.0162 0.0167 0.0172 0.0178 0.0183 0.0189 0.0195 0.0201 0.0208 0.0214 0.0221 0.0227 0.0234 0.0242 0.0249 0.0257 0.0265 0.0273 0.0281 0.0289 0.0298 0.0307 0.0315 0.0325 0.0336 0.0345 0.0356 0.0367 0.0378 0.0389 0.04 0.0412 0.0424 0.0437 0.045 0.0463 0.0476 0.049 0.0504 0.0519
39.31 40.66 42.05 43.46 44.89 46.36 47.85 49.37 50.93 52.51 54.13 55.78 57.47 59.18 60.94 62.73 64.56 66.43 68.33 70.28 72.27 74.31 76.38 78.51 80.67 82.89 85.16 87.47 89.84 92.26 94.74 97.27 99.86 102.5 105.2 108 110.8 113.7 116.7 119.7 122.8 126 129.3 132.6 136 139.5 143.1 146.8 150.5 154.4 158.3 162.3 166.5 170.7 175
0.827 0.829 0.831 0.833 0.835 0.837 0.838 0.84 0.842 0.844 0.846 0.848 0.851 0.853 0.855 0.857 0.859 0.861 0.863 0.866 0.868 0.87 0.872 0.875 0.877 0.879 0.882 0.884 0.887 0.889 0.892 0.894 0.897 0.899 0.902 0.905 0.908 0.91 0.913 0.916 0.919 0.922 0.925 0.928 0.931 0.934 0.937 0.94 0.944 0.947 0.95 0.954 0.957 0.961 0.964
0.016 0.016 0.017 0.018 0.018 0.019 0.019 0.02 0.021 0.021 0.022 0.023 0.023 0.024 0.025 0.026 0.026 0.027 0.023 0.029 0.03 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.038 0.039 0.04 0.041 0.042 0.044 0.045 0.046 0.475 0.019 0.05 0.052 0.053 0.055 0.056 0.058 0.059 0.061 0.063 0.064 0.066 0.068 0.07 0.072 0.074 0.076 0.078
0.016 0.016 0.017 0.018 0.019 0.019 0.02 0.02 0.021 0.022 0.023 0.023 0.024 0.025 0.025 0.026 0.027 0.028 0.029 0.029 0.03 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.039 0.04 0.041 0.042 0.043 0.044 0.046 0.047 0.048 0.02 0.051 0.053 0.054 0.056 0.057 0.059 0.061 0.062 0.064 0.066 0.068 0.069 0.071 0.073 0.075 0.077 0.08
0.23 0.24 0.43 0.26 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.4 0.41 0.42 0.43 0.45 0.46 0.47 0.49 0.5 0.52 0.53 0.55 0.56 0.58 0.6 0.62 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.82 0.84 0.86 0.89 0.91 0.94 0.96 0.99 1.01 1.04 1.07 1.1 1.13
12 12.4 12.8 13.2 13.6 14.1 14.5 15 15.5 16 16.5 17 17.5 18.1 18.6 19.2 19.8 20.4 21 21.7 22.4 23 23.7 24.5 25.2 25.9 26.7 27.5 28.3 29.2 30 30.9 31.8 32.7 33.7 34.6 35.6 36.7 37.7 38.8 39.9 41 42.1 43.3 44.5 45.8 47 48.3 49.7 51 52.4 53.8 55.3 56.8 58.3
0.47 0.49 0.5 0.52 0.54 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.76 0.78 0.8 0.83 0.85 0.88 0.91 0.93 0.96 0.99 1.02 1.05 1.08 1.12 1.15 1.18 1.22 1.25 1.29 1.33 1.36 1.4 1.44 1.48 1.53 1.57 1.61 1.66 1.71 1.75 1.8 1.85 1.9 1.96 2.01 2.06 2.12 2.18 2.24 2.3
p ft of water 0.5 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1 1 0 1.1 1.1 1.1 1.2 1.2 1.2 1.3 1.3 1.3 1.4 1.4 1.5 1.5 1.5 1.6 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2 2 2.1 2.2 2.2 2.3 2.3 2.4 2.5 2.6 2.6
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R.Rajvaidya & S.P.S. Rajput
T
T
WS
hS
vS
p
p
p psia
p mm of Hg
p inch of Hg
o
C
K
kJ/kg
m3/kg
bar
ata
41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0
315 315 316 316 317 317 318 318 319 319 320 320 321 321 322 322 323 323
kg/kg of dry air 0.0534 0.055 0.0566 0.0582 0.0599 0.0616 0.0634 0.0652 0.0671 0.0691 0.0771 0.0731 0.0752 0.0774 0.0796 0.0819 0.0842 0.0866
179.5 184.1 188.7 193.5 198.4 203.5 208.6 213.9 219.4 224.9 230.6 236.5 242.5 248.7 255 261.6 268.2 275.1
0.968 0.972 0.976 0.98 0.984 0.988 0.992 0.996 1.000 1.005 1.009 1.014 1.018 1.023 1.028 1.033 1.038 1.043
0.08 0.082 0.084 0.086 0.089 0.091 0.093 0.096 0.098 0.101 0.103 0.106 0.109 0.112 0.114 0.117 0.12 0.123
0.081 0.094 0.086 0.088 0.092 0.093 0.095 0.098 0.1 0.103 0.105 0.108 0.111 0.114 0.117 0.12 0.123 0.126
1.16 1.19 1.22 1.25 1.29 1.32 1.35 1.39 1.43 1.46 1.5 1.54 1.58 1.62 1.66 1.7 1.74 1.79
59.9 61.5 63.1 64.8 66.5 68.2 70 71.8 73.7 75.6 77.6 79.6 81.6 83.7 85.8 88 90.2 92.5
2.36 2.42 2.48 2.55 2.62 2.69 2.76 2.83 2.9 2.98 3.05 3.13 3.21 3.29 3.38 3.46 3.55 3.64
p ft of water 2.7 2.7 2.8 2.9 3 3 3.1 2.2 3.3 3.4 3.5 3.5 3.6 3.7 3.8 3.9 4 4.1
(18) Now, the modeling results values.
RESULTS AND DISCUSSIONS Table 2: [14]:- For Automobile Speed Velocity; V1 = 60 Km/Hr tdb10C
φ1
W1 kg/kg of dry air
30
350C
400C
15% 20% 25% 15% 20% 25% 15% 20% 25%
0.00398 0.005327 0.006673 0.00529 0.00708 0.0089 0.00696 0.00932 0.01169
M1 kg/min. 280.60 279.85 279.24 275.68 274.35 273.79 270.69 269.56 268.59
Ma kg/min 279.436 278.36 277.38 274.23 273,02 271.39 268.82 267.07 265.48
W2
t2 0 C
φ2
300C 290C 290C 330C 350C 330C 38.60C 390C 39.40C
15.5% 21% 28.1% 36% 21.5% 29% 17.69% 22.5% 24%
kg/kg of dry air
0.004367 0.005716 0.00706 0.005691 0.007479 0.009275 0.007303 0.00973 0.01201
As this is a result from the theoretical calculation which shows that, when the velocity of automobile is 60Km/hr and the ambient air of a relative humidity range from 15% to 25% which is bleeding in to the inlet ETR face duct with the temperature range of 30℃ to 40℃ (considering for the month march), this ambient air passes through cooling pad material kept in the ETR material chamber, the outlet air from the ETR to the automobile cabin, the temperature range is from 29℃ to 39.40C and relative humidity range is from15.5%-36% .Drop in the ambient temperature is by 0.6℃ to 1℃ and simultaneously increase in relative humidity by 0.5% to 11%.
CONCLUSIONS These readings justify that drop in temperature is less but the percentage increase in relative humidity is moderate, and it is a complex result according to our expectation as it is throughout theoretical. The result also point attention on the speed of the automobile, which has been increase.
Thermodynamics Modeling of Automobile Evaporative air Conditioning (Evaporative Test Rig) with Result and Discussion, When Automobile Velocity is 60km/Hr
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